MAT 244 Ordinary Differential Equations
Instructors: Mohammad Ali Niksirat, Yanli Song & Nicholas Hoell
Course Website: http://www.math.toronto.edu/nhoell/MAT244.html
Office Hours: TBD & By Appointment
You should contact the course instructor in the section
you are enrolled in for particular details/questions throughout the term.
Technical Details
Welcome! Make sure you are aware of the following University details regarding this
course.
• Prerequisites: MAT135Y1/(MAT135H1, MAT136H1)/MAT137Y1/MAT157Y1,
MAT223H1/MAT240H1
• Corequisites: MAT235Y1/MAT237Y1
• Exclusion: MAT267H1
• Distribution Requirement Status: This is a Science course
• Breadth Requirement: The Physical and Mathematical Universes (5)
Teaching Assistants
Part of your tuition helps pay for University resources, one of the most valuable of which
is time you can get one-on-one help from very knowledgable teaching assistants. I encourage you to make use of them. This semester the TAs are holding office hours each
weekday. These are as follows
• Craig Sinnamon on Mondays 1–2 in BA6283
• Dan Fusca on Tuesdays 5–6 in BA6283
• Kyle Thompson on Wednesdays 12–1 in BA6283
• Shuangjian Zhang on Thursdays 4–5 in GB220
• Hareem Naveed on Fridays 12–1 in GB221
Tutorials
There are no tutorial sections for this course.
Required Text
Our required text will be “Elementary Differential Equations and Boundary Value Problems"
by William Boyce and Richard DiPrima, published by Wiley. We will be using the 10th
edition. Other editions are fine but problem set question numbers will only correspond to the 10th edition. The substantive material hasn’t changed across editions but
there are variations, particularly with regard to problem numbers so be aware of this if
you decide to use an older edition.
Online Textbook
Instead of obtaining the physical textbook, you can opt to obtain the online textbook,
which is cheaper than the (new) textbook. You can print and read it using a tablet app:
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Wiley e-Textbook
It is also available through CourseSmart:
CourseSmart e-Textbook
In my experience, textbooks on introductory differential equations vary. You may find
the online texts listed below may be more enjoyable that the required text. Explore!
Alternative (More Advanced) Texts
More mathematically inclined students may enjoy "Ordinary Differential Equations" by
V.I. Arnold, published by MIT press. This is an excellent (and affordable), far more advanced, book on material appearing throughout this course. Those wishing to learn
more of the theoretical underpinnings and extensions of topics in this course cannot go
wrong with this book.
In the same vein as the book by Arnold is ”Differential Equations, Dynamical Systems, and
Linear Algebra" by Hirsch and Smale by Academic Press. Again, this is a more advanced
treatment but is also considered a classic.
Online Resources/Texts
I also recommend the free text by Gabriel Nagy available at
http://math.msu.edu/~gnagy/teaching/ode.pdf
Grading
Grades will be based according to two midterm exams and a final exam. Your final grade
in the course will be determined by the following
• Lowest Midterm 20%, Highest Midterm 30%
• Final Exam 50%
Optional problem sets will cover concepts discussed in the lectures as well as some material presented in the text. Problem sets will be offered a few times during the semester,
but not for credit. Working through the recommended problems is essential to success
in this course. The test dates will be as follows
• Test 1: February 25, 19:00-20:30
• Test 2: March 15, 19:00-20:30
Note on Exams
No electronic devices/aids will be allowed during the exams. It is the students’ responsibility to ensure that the allotted exam time is available.
Questions & Concerns
It is University policy that instructors need only reply to emails sent from University
email accounts. Acceptable emails are of the form student@utoronto.ca,
topstudent@math.toronto.edu, etc. We might not ever reply to a non-University email
address (those from addresses like, say, studentwhoseemaildidntgetreturned@hotmail.com
or studentwhodidntreadthesyllabus@gmail.com). As for email etiquette, sending technical mathematics questions is fine if they are very short but I really encourage you to
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save longer questions for the beginning Q&A part of the following lecture, or ask during
office hours, since this will offer the greatest benefit to the largest number of students.
Blackboard
We tend to not use Blackboard except for sending out email to the class or when entering
marks on tests and quizzes. For any important course information you should look to
the course web site, part of my Toronto site, listed at the front of this syllabus.
Academic Integrity (Important)
Cheating (including plagiarism) is very serious and, consequently, will be taken very seriously. Cheating can result in failure or worse. Don’t do it! I caution you I am extremely
diligent in pushing for the maximum possible penalties for those found cheating. Collaboration on the homework problem sets is fine, in fact I encourage it since discussing
problems with your peers helps bolster your problem solving abilities, but the write-up
should be done on your own, by your own hand. Any collusion during quiz or test situations will be thoroughly punished.
Attendance
I will not be taking attendance, however the best & easiest way to stay on top of the material is by attending lectures and asking questions, so I encourage good attendance &
participation.
Late Assignment Policy
No late assignments will be accepted without prior confirmation.
Prerequisites
Regardless of any formal requisites students need to be comfortable with standard calculus concepts like
• The difference between an antiderivative and a definite integral
• The fundamental theorem of Calculus, in its many guises
• Partial derivatives
• Various notations for partial derivatives
• Matrix arithmetic and determinants, eigenvalues, eigenvectors, diagonalization,
etc. This is a crucial part of the course that many students have trouble remembering how to do. Save yourself the headache and brush off your book on linear
algebra now!
Goals & Course Description
Congratulations for having read this far! This summer, we will cover a variety of topics
within ordinary differential equations and explore some of the recurring themes in the
subject. Differential equations is a subject best learned through case studies and we will,
by examining several well-known equations from physics, encounter general methodology for analyzing qualitative and quantitative behaviour of their solutions. Part of
the course involves learning a “bag of tricks" which can be useful for attacking differential equations based on their “type". Other parts of the course are about understanding
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qualitative features of solutions, regardless of whether one can quantitatively/explicitly
solve the equation in question.
The Menu
We will keep, roughly, to the following schedule (dates refer to week containing the Monday falling on the given MM/DD). Moreover, the corresponding chapters in Boyce/DiPrima
10th edition (listed as BD) are listed as a rough indication of the corresponding parts of
the textbook covered that week:
• 1/11- Taxonomy of ODE & initial conditions. Direction Fields. Some solutions.
Introduction to linear equations. BD Chapter 1.
• 1/18- First oder linear equations equations. Integrating factors. Separable equations. BD Chapter 2.
• 1/25- Autonomous equations. Population equations. Some basic modelling. BD
Chapter 2.
• 2/1- Second order equations. Homogeneous equations with constant coefficients.
The Wronskian. BD Chapter 3.
• 2/8- The Characteristic equations. BD Chapter 3.
• 2/15- Undetermined coefficients and parameter variation. BD Chapter 3.
• 2/22 - Equations of higher order. BD Chapter 4.
• 2/29- Linear systems and Fundamental Matrices. BD Chapter 7.
• 3/7 - Phase Portraits and eigenvalues. BD Chapter 7.
• 3/14 - Nonlinear problems and linearizing.BD Chapter 9.
• 3/21- More on nonlinearity. BD Chapter 9.
• 3/28 - Power series methods, time permitting. BD Chapter 5.
• 4/4- Buffer & Review.
In the above, Chapter numbers refer to the fifth edition of Haberman’s text and quite
often we will cover only certain sections within a given chapter.
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